Deep learning (DL) applications have redefined the state of the art performance for bearing data driven fault detection and identification, a crucial demand of modern industrial systems. The success of DL methods, in the field of automatic fault diagnosis, is based on the usage of raw sensor data, contrary to conventional machine learning (ML) approaches in which manual extraction of features, from prior expertise knowledge, is necessary. However, DL approaches require a large amount of training data samples to be effective and to outperform competitive ML methods. In this study, we overcome this drawback by proposing the Attentive Dense Convolutional Neural Network (ADCNN), a DL network, which considers the temporal coherence of the data samples, by the combination of Dense Convolutional blocks with an attention mechanism. The proposed neural scheme has fewer unknown learning parameters and achieves accurate results with less training data as it appears from simulation cases on two famous rolling bearings fault detection benchmarks.